Transcript Trigonometric Ratios

Trigonometric
Ratios
A RATIO is a comparison
of two numbers. For
example;
boys to girls
cats : dogs
right : wrong.
In Trigonometry, the
comparison is between
sides of a triangle.
Trig. Ratios
Name
“say”
Abbreviation
Abbrev.
Ratio of an
angle
measure
Sine
Cosine
tangent
Sin
Cos
Tan
Sinθ = opposite side cosθ = adjacent side
hypotenuse
hypotenuse
tanθ =opposite side
adjacent side
Three Trigonometric Ratios
• Sine – abbreviated ‘sin’.
– Ratio: sin θ = opposite side
hypotenuse
Θ this is the symbol for
an unknown angle
measure. It’s name is
‘Theta’.
• Cosine - abbreviated ‘cos’.
– Ratio: cos θ = adjacent side
hypotenuse
• Tangent - abbreviated ‘tan’.
– Ratio: tan θ = opposite side
adjacent side
Easy way to remember trig
ratios:
SOH CAH TOA
Let’s practice…
Write the ratio for sin A
B
Sin A = o = a
h c
c
Write the ratio for cos A
a
C
b
Cos A = a = b
h c
A
Write the ratio for tan A
Let’s switch angles:
Find the sin, cos and
tan for Angle B:
Sin B = b
c
Tan A = o = a
a b
Cos B = a
c
Tan B = b
a
I want to find
Use these calculator keys
Ratio of sides as a decimal
Regular keys
A missing side
SIN
COS
TAN
Angle measure
SIN-1
COS-1
TAN-1
Make sure you
have a calculator…
To set your calculator to DEGREE:
MODE (next to 2nd button)
Degree (third line down… highlight it)
Enter
2nd
Quit
Let’s practice…
Find an angle that has a
tangent (ratio) of 2
C
2cm
B
3
Round your answer to the
nearest degree.
3cm
A
Process:
I want to find an ANGLE
I was given the sides (ratio)
Tangent is opp
adj
TAN-1(2/3) = 34°
Practice some more…
Find tan A:
Tan A = opp/adj = 12/21
24.19
A
12
Tan A = .5714
21
Find tan A:
8
Tan A = 8/4 = 2
4
A
Trigonometric Ratios
• When do we use them?
– On right triangles that are NOT 45-45-90 or
30-60-90
Find: tan 45
1
Why?
tan = opp
adj
Using trig ratios in equations
Remember back in 1st grade when you had
to solve:
(6)12 = x (6)
What did you do?
6
72 = x
Remember back in 3rd grade when x was in
the denominator?
(x)12 = 6 (x)
What did you do?
x
__
__
12x = 6
x = 1/2
Ask yourself:
In relation to the angle,
what pieces do I have?
34°
15 cm
Opposite and hypotenuse
Ask yourself:
x cm
What trig ratio uses
Opposite and Hypotenuse?
SINE
Set up the equation and solve:
(15) Sin 34 = x (15)
15
(15)Sin 34 = x
8.39 cm = x
Ask yourself:
In relation to the angle,
what pieces do I have?
53°
12 cm
Opposite and adjacent
x cm
Ask yourself:
What trig ratio uses
Opposite and adjacent?
tangent
Set up the equation and solve:
(12)Tan 53 = x (12)
12
(12)tan 53 = x
15.92 cm = x
x cm
Ask yourself:
In relation to the angle,
what pieces do I have?
Adjacent and hypotenuse
68°
18 cm
Ask yourself:
What trig ratio uses
adjacent and hypotnuse?
cosine
Set up the equation and solve:
(x) Cos 68 = 18 (x)
x
(x)Cos
18
_____68 =_____
cos 68 cos 68
X = 18
X = 48.05 cm
cos 68
42 cm
22 cm
θ
This time, you’re looking for theta.
Ask yourself:
In relation to the angle, what pieces
do I have? Opposite and hypotenuse
Ask yourself:
What trig ratio uses opposite
and hypotenuse? sine
Set up the equation (remember you’re looking for theta):
Sin θ = 22
42
Remember to use the inverse function
when you find theta
Sin -1 22 = θ
42
31.59°= θ
You’re still looking for theta.
θ
Ask yourself:
22 cm
17 cm
What trig ratio uses the parts I
was given? tangent
Set it up, solve it, tell me what you get.
tan θ = 17
22
tan -1 17 = θ
22
37.69°= θ
Your assignment
Cannibal
Trignometry wksht